BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Ambitoric structures and extremal Kahler  orbi-surfaces with b_2(M
 )=2. - Vestislav Apostolov (Université du Québec à Montréal)
DTSTART:20120410T103000Z
DTEND:20120410T113000Z
UID:TALK36834@talks.cam.ac.uk
CONTACT:Dr. J Ross
DESCRIPTION:I will discuss an explicit resolution of the existence\nproble
 m for extremal  Kahler metrics on toric 4-orbifolds $M$ with second Betti 
 number equal to 2.  \n\nMore precisely\, I will show that $M$ admits such 
 a metric if and only if its rational Delzant polytope (which is a labelled
  quadrilateral) is K- polystable in the relative\, toric sense (as studied
  by S. Donaldson\, G. Sz\\'ekelyhidi et al.). Furthermore\, in this case\,
  the extremal Kahler metric is ambitoric\, i.e.\, compatible with a confor
 mally equivalent\, oppositely  oriented toric Kahler metric\, which turns 
 out also to be extremal.  \n\nAmong the explicit  extremal Kahler metrics 
 obtained\,   there are conformally Einstein examples  which are Riemannian
  analogues of the exact solutions of the Einstein equations in General Rel
 ativity\, found by R. Debever\, N. Kamran\, and R. McLenaghan. This is a j
 oint work with D. Calderbank and P. Gauduchon.\n
LOCATION:MR2
END:VEVENT
END:VCALENDAR